Vector operator

A vector operator is a type of differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and curl:
operatorname{grad} equiv nabla
operatorname{div} equiv nabla cdot
operatorname{curl} equiv nabla times

The Laplacian is

nabla^2 equiv operatorname{div} operatorname{grad} equiv nabla cdot nabla

Vector operators must always come right before the scalar field or vector field on which they operate, in order to produce a result. E.g.

nabla f
yields the gradient of f, but
f nabla
is just another vector operator, which is not operating on anything.

A vector operator can operate on another vector operator, to produce a compound vector operator, as seen above in the case of the Laplacian.

See also

Further reading

  • H. M. Schey (1996) Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, ISBN 0-393-96997-5.

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